Yes, there is a risk of failure involved with anything electrical, but I don't see why anyone would consider chaining extension cords inherently dangerous enough to ban. It increases the number of connections, but that's a miniscule risk compared to the 5+ connections an extension cord might have on its own. The only significant risk I know is people disregarding the max amperage rating of everything in that chain.

For anecdotal experience, I've had both extension cords and wall plugs fail (nothing serious thankfully, but they did get a bit melted), but in those cases it had nothing to do with my extension cord chains, but rather an internal connection failure.